Page 212 - Shigley's Mechanical Engineering Design

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Deflection and Stiffness 187

EXAMPLE 4–17 Specify the diameter of a round column 1.5 m long that is to carry a maximum load
estimated to be 22 kN. Use a design factor n d = 4 and consider the ends as pinned
(rounded). The column material selected has a minimum yield strength of 500 MPa and
a modulus of elasticity of 207 GPa.
Solution We shall design the column for a critical load of

P cr = n d P = 4(22) = 88 kN
Then, using Eq. (4–51) with C = 1 (see Table 4–2) gives
64P cr l 64(88)(1.5) 10 3
2 1/4 2 1/4 3 1/4
d = = (10 ) = 37.48 mm
3
3
π CE π (1)(207) 10 9
Table A–17 shows that the preferred size is 40 mm. The slenderness ratio for this size is
3
l l 1.5(10 )
= = = 150
k d/4 40/4
To be sure that this is an Euler column, we use Eq. (5–51) and obtain
l 2π CE 2π (1)(207) 10
2 1/2 2 1/2 9 1/2
= = = 90.4
k S y 500 10 6
1
which indicates that it is indeed an Euler column. So select
Answer d = 40 mm

EXAMPLE 4–18 Repeat Ex. 4–16 for J. B. Johnson columns.
Solution (a) For round columns, Eq. (4–46) yields
1/2
S y l 2
Answer d = 2 P cr + (4–53)
2
πS y π CE
(b) For a rectangular section with dimensions h ≤ b, we find
Answer b = P cr 2 h ≤ b (4–54)
3l S y
hS y 1 −
2
π CEh 2

EXAMPLE 4–19 Choose a set of dimensions for a rectangular link that is to carry a maximum compres-
sive load of 5000 lbf. The material selected has a minimum yield strength of 75 kpsi
and a modulus of elasticity E = 30 Mpsi. Use a design factor of 4 and an end condi-
tion constant C = 1 for buckling in the weakest direction, and design for (a) a length
1
of 15 in, and (b) a length of 8 in with a minimum thickness of in.
2